Methods to Finding Displacement
Non-Mathematical Method for Vector Addition
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Scale Diagram Method
Used for any given vectors but it’s accuracy depends on how well the diagram is constructed
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Determine an appropriate scale and draw a compass
Draw the first vector to scale (in the proper direction)
Start the tail of the next vector from the tip of the first vector – continue until all the vectors are drawn
Draw the resultant vector, Δdr, from the tail of the first vector to the tip of the last vector.
Measure the length of your resultant vector and use the scale to determine the actual displacement.
Use a compass to determine the direction of the resultant vector.
Write a concluding statement for the displacement (express with magnitude, units and direction)
Mathematical Analysis of Vector Addition
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Colinear vectors – those that follow the same straight line back and forth
1. Assign one direction to be + and the opposite direction to be –. Indicate at the beginning of the
question.
2. Take each vector and express them as positive and negative numbers based on 1.
3. Sum the vectors together
4. Re-write the vector with a direction instead of a positive or negative sign
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Motion in Two Dimensions:
1. Provide a rough sketch of all vectors added together and indicate the resultant displacement vector.
2. Examine the diagram to determine the correct mathematical approach to solving the problem. Hints:
a. Construct a right triangle if possible. It may be necessary to simplify the diagram by taking into
consideration collinear vectors.
b. If a right triangle, use Pythagorean theorem and trigonometric ratios to solve for mag and dir.
c. If it is a non-right angle triangle, use sine law and cosine law to solve for mag and dir.
Pythagorean Theorem: c2 = a2 + b2
Trig Ratios: SOH CAH TOA
Sine law: _ a = ___b = ___c
sin A
sin B
sin C
Cosine Law:
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c2 = a2 + b2 – 2ab cos C
Using Components:
Useful when there are three or more vectors to be added
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Assign a positive and negative direction to the x- and y- axis
Separate each vector into its x-components and y-components using trigonometry
Add all x-components together, add all y-components together
Create a right angled triangle
Use Pythagorean theorem and trigonometry to solve for magnitude and direction